The purpose of this study is to determine whether nitazoxanide (an investigational drug) is safe and effective for treating persons with cryptosporidiosis and HIV infection. Cryptosporidiosis is a parasite that infects the intestines of people; it can be a significant problem for persons with HIV infection. In previous studies, nitazoxanide was shown to reduce the number of bowel movements in persons with cryptosporidiosis, but more information is needed.